Mechanical and electronic properties of ferromagnetic ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ using ultrafast coherent acoustic phonons

Ultrafast two-color pump-probe measurements, involving coherent acoustic phonon waves, have provided information simultaneously on the mechanical properties and on the electronic structure of ferromagnetic ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$. The elastic constants $C_{11}$ of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ $\left(0.03\le x\le 0.07\right)$ are observed to be systematically smaller than those of GaAs. Both $C_{11}$ and $V_{\text{s}}$ measured in ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ are found to increase with temperature $\left(78\text{K}\le T\le 295\text{K}\right)$, again in contrast to the opposite behavior in GaAs. In addition, our experimental results indicate a small blueshifting of the fundamental band gap of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ as Mn concentration increases.

Figure 1

(a) Pump-probe response of ${\text{Ga}}_{0.95}{\text{Mn}}_{0.05}\text{As}/\text{LT-GaAs}/\text{GaAs}$ at 78 K for the probe wavelength 830 nm; (b) derivative of envelope of oscillations $\left|{\left(\Delta R/R\right)}_{\text{env}}\right|$ as a function of delay time. Inset: the subtracted oscillatory response and its envelope. The regimes determined by the GaMnAs and LT-GaAs layers are indicated by horizontal arrows in the inset, respectively.

Figure 2

(a) Oscillation period $T_{\text{p}}$ at 800 nm and (b) elastic constant $C_{11}$ as a function of temperature $T$ for ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$, LT-GaAs, and GaAs. Solid lines are linear fits for GaAs and ${\text{Ga}}_{0.97}{\text{Mn}}_{0.03}\text{As}$, respectively.

Figure 3

Charge-density difference $\Delta \rho$ for (a) bulk GaAs and (b) ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ $\left(x=0.03\right)$ in the {110} plane which contains a zigzag atomic chain. $\Delta \rho$ is defined as the charge density of a strained crystal minus the charge density of an unstrained crystal. The applied strain is ${\epsilon }_1=-0.01$. Contour steps are $4\times {10}^{-4}\text{e}/{\text{Å}}^3$ and solid (dashed) contours indicate charge accumulation (depletion).

Figure 4

Oscillation period $T_{\text{p}}$ as a function of the wavelength $\lambda$ of probe light for ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$, LT-GaAs, and GaAs at 78 K. Dashed line represents the position of the critical point $E_0$ of GaAs.

Figure 5

(a) Damping time $\tau$ as a function of the wavelength $\lambda$ of probe light for ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$, LT-GaAs, and GaAs at 78 K. Dashed line represents the position of the critical point $E_0$ of GaAs. In (b), curves for ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ are shifted downward with increasing x to more clearly show the blueshift.